Power amplifiers in communication systems are a main source of non-linearity, e.g., input signals are generally distorted during amplitude modulation, especially as the power nears the saturation level of the amplifier. Another source of non-linearity is memory effects. Generally, memory effects cause additional odd order, e.g., 3rd, 5th, 7th, etc., intermodulation distortion. Memory effects may include, but are not limited to, power amplifier self-heating and decoupling of the power amplifier from a power supply. In self-heating, as the power amplifier power level increases, heat is built up in the devices used in the power amplifier. Conversely, a decrease in the power level causes cooling of the devices. Such heating and cooling of the devices generally results in odd order distortion.
One method for reducing distortion and non-linearity is to operate the power amplifier in a linear region below its maximum power capacity, i.e., backing off. However, this would require a larger amplifier than would otherwise be the case, which makes the system less efficient and more expensive. This problem is made more severe by modern wide bandwidth modulation schemes, such as CDMA, WCDMA and UMTS, which employ signals with large random signal peaks. Therefore, it is highly desirable to reduce distortion while maintaining amplifier efficiency by reducing distortion without simply making the amplifier bigger. One approach is to pre-distort the input signal prior to amplification to correct for amplifier nonlinearities.
There are many methods for pre-distorting signals to linearize power amplifiers. Typically, a pre-distortion unit is placed between the input signal and the power amplifier, where the pre-distortion unit receives signals for distorting the input signal based on feedback signals from the amplifier output signal. Thus, before the signal is amplified, an estimate is made of the manner in which the amplifier will non-linearly distort the particular input signal by amplifying that signal. The signal to be amplified is then “pre-distorted” by applying to it a transformation in a manner estimated to be complementary to the non-linearity which the amplifier itself will apply as it amplifies the signal. Ideally, the pre-distorting transformation is cancelled out by the amplifier's non-linearity, resulting in an undistorted, amplified output signal. In general, conventional pre-distortion to reduce non-linearity was performed at baseband in the digital domain. But note that the non-linearity introduced by the power amplifier is analog and in the RF domain. The resulting necessity to digitize and analyze the non-linearity at baseband results in unnecessary power consumption and complication.
An alternative to conventional pre-distortion techniques and systems is disclosed in commonly-assigned U.S. application Ser. No. 11/484,008, filed Jul. 7, 2006 (hereinafter the '008 application), now U.S. Pat. No. 7,844,014, the contents of which are incorporated by reference in their entirety, wherein the pre-distortion is performed in the RF domain rather than at baseband. In the '008 application, an error signal is calculated through comparison of a properly-scaled version of the amplified output signal from the power amplifier to the power amplifier's input signal. Should the power amplifier be perfectly linear, this error signal is zero. However, real-world power amplifiers will produce some non-linearity in the output signal such that the error signal is non-zero.
To pre-distort the power amplifier input signal in the RF domain, the input signal is typically multiplied with a pre-distorting signal. For example, an RF input signal may be represented by the real part of {R(t)*exp(jωct)}, where R(t) is the complex envelope, j is the imaginary unit, ωc is the angular frequency for the RF carrier bearing the complex envelope modulation, and t is time. It may thus be seen that the pre-distortion signal is a baseband signal because the pre-distortion signal is a function of the complex envelope R(t) and not of the RF carrier. In that regard, a pre-distortion signal may be represented by a Taylor series expression: α1+α2*R(t)+α3*R(t)2+α4*R(t)3+ . . . , where the alpha symbols represent pre-distortion coefficients, which may also be denoted as pre-distortion weights. Upon multiplication of such a pre-distortion signal with the RF input signal, the resulting pre-distorted RF signal that is produced becomes the real part of {[α1*R(t)+α2*R(t)2+α3*R(t)3+α4*R(t)4+ . . . ]*exp(jωct). It is this pre-distorted RF signal that is supplied as an input signal to the power amplifier. The final envelope power in the pre-distorting signal depends upon the complexity of the design and desired precision. For example, suppose the final power in the series expression is five, corresponding to R(t)5. In such an embodiment, it may be seen that a signal generator generating the pre-distorting signal must solve for six coefficients in the Taylor series, ranging from α1 to α6.
The envelope term associated with each pre-distortion weight in the pre-distortion signal may be designated as a corresponding monomial “basis” function. Thus, the monomial basis function associated with pre-distortion weight α1 is R(t)0, the basis function associated with pre-distortion weight α2 is R(t), the basis function associated with pre-distortion weight α3 is R(t)2, and so on. The pre-distortion weights associated with the basis functions may be determined in a variety of fashions. In an example analytical approach, a signal generator may include a correlator for each pre-distortion weight. Each correlator correlates the error signal with the basis function corresponding to the correlator's pre-distortion weight. Although analytically correct in theory, it may be shown that such a selection of monomial basis functions will not typically produce desirable real-world results because the convergence time to a solution is too long. To enhance the convergence speed, the '008 application discloses that each basis function may be an orthonormal polynomial formed from the above-discussed mononomial basis functions.
Although the '008 application discloses a power amplifier linearization technique that has lower bandwidth demands, higher precision, and lower power consumption as compared to conventional schemes that perform their distortion in the digital baseband domain, correlation in the RF analog domain to generate the coefficients can lead to mismatches. This mismatch occurs because a correlation determines the pre-distortion weights for the basis functions used to create a pre-distortion signal for pre-distorting the RF input signal. A pre-distortion signal must then be created based upon these determined pre-distortion weights by multiplication with the basis functions. A second multiplication is then required to multiply the input signal with the resulting pre-distorting signal. Because of circuit non-idealities and other effects, the pre-distorting signal may have coefficients that are slightly different from the analog coefficients that result from the correlation. Moreover, even if such non-idealities could be eliminated, improvements in convergence speed are desirable.
Regardless of whether or not correlation is used to produce a pre-distorting signal, the input signal is distorted to form the pre-distorting signal based upon an analysis of an error signal that results from comparing a delayed version of the input signal to a version of the amplified output signal. This delayed version of the input signal should be delayed such that the delay matches a group delay introduced in the amplified output signal by the power amplifier. Small errors in such delay matching as well as gain and/or phase imbalances between the compared signals results in less-than-optimum linearization.
Accordingly, there is a need in the art for improved error signal formation techniques.